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Stars
… how I wonder what you are.
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Goals
• Stars are Suns.
• Are they:
–
–
–
–
–
Near? Far?
Brighter? Dimmer?
Hotter? Cooler?
Heavier? Lighter?
Larger? Smaller?
• What categories can we place them in?
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Concept Test
•
If Star A has a parallax of 2 arcseconds, and Star
B has a parallax of 0.25 arcseconds:
a. Star A is closer to us than Star B. Both are farther
from us than 1 pc.
b. Star A is closer to us than Star B. Both are closer to us
than 1 pc.
c. Star A is closer to us than 1 pc. Star B is farther than 1
pc.
d. Star B is closer to us than 1 pc. Star A is farther than 1
pc.
e. Star B is closer to us than Star A. Both are farther
away than 1 pc.
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Distances
1
Distance (in parsecs) 
parallax (in arcsec)
• Closest star: Proxima Centauri
parallax = 0.76 arcsec
Distance = 1.3 pc or 4.3 lightyears
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Terms
• Brightness = How
intense is the light I
see from where I am.
– Magnitude is
numerical term for this.
• Luminosity = how
much light is the thing
really giving off.
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Magnitude
Scale
• The SMALLER the
number the BRIGHTER
the star!
– Every difference of 1
magnitude = 2.5x brighter or
dimmer.
– Difference of 2 magnitudes
= 2.5x2.5 = 6.3x brighter or
dimmer
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Magnitude vs. Brightness
Mag.
Difference
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Factors of 2.5
2.51 = 2.5
Brightness
Diff.
2.5
2
2.52 = 2.5 X 2.5
6.3
3
2.53 = 2.5 X 2.5 X 2.5
16
4
2.54 = 2.5 X 2.5 X 2.5 X 2.5
40
5
2.55 = 2.5 X 2.5 X 2.5 X 2.5 X 2.5
100
6
2.56 = 2.5 X 2.5 X 2.5 X 2.5 X 2.5 X 2.5
250
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Star light, star
bright
• Sirius is magnitude -1.5
Polaris is magnitude 2.5
• Is Sirius really more
luminous than Polaris?
• No, Sirius is just closer.
• Example: light bulbs.
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Apparent and Absolute
• Apparent Magnitude = brightness (magnitude) of a
star as seen from Earth.  m
– Depends on star’s total energy radiated (Luminosity) and
distance
• Absolute Magnitude = brightness (magnitude) of a
star as seen from a distance of 10 pc.  M
– Only depends on a star’s luminosity
 distance
m  M  5log 10 
 10pc



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example
 distance
m  M  5log 10 
 10pc



• Our Sun:
– m = -26.8,
– distance = 4.8 x 10-6 pc
So: M = 4.8
• Polaris:
– m = 2.5,
– distance = 132 pc
So: M = -3.1
• Polaris is 1500 times more luminous than the Sun!
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Concept Test
•
Star
Distance
m
A
5 pc
1.0
B
10 pc
2.5
C
20 pc
-1.0
M
The most likely absolute magnitudes (M) for each is:
a.
b.
c.
d.
e.
A = 2.5, B = -2.5, C = 2.5
A = 2.5, B = 2.5, C = -2.5
A = -2.5, B = 2.5, C = 2.5
A = 2.5, B = 2.5, C = 2.5
None of the above.
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Stellar Temperatures
Hot
Stellar Spectra
How hot are stars?
• Thermal radiation
and temperature.
• Different stars
have different
colors, different
stars are
temperatures.
• Different temp,
different trace
compositions
Cool
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Spectral
Classification
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Stellar Masses
How massive are stars?
• Kepler’s Laws – devised for the planets.
• Apply to any object that orbits another object.
• Kepler’s Third Law relates:
– Period: “how long it takes to orbit something”
– Semimajor axis: “how far you are away from that something”
– Mass: “how much gravity is pulling you around in orbit”
3
a
P 
M
2
• Where M is the Total Mass.
• Can calculate the mass of stars this way.
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Binary Stars
• Most stars in the sky
are in multiple
systems.
• Binaries, triplets,
quadruplets, etc….
– Sirius
– Alcor and Mizar
– Tatooine
• The Sun is in the
minority by being
single.
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NPOI Observations of Mizar A
(1 Ursa Majoris)
0.005 arcsec
Orbital Phase: 000o
Mizar, 88 light years distant, is the middle star in the handle of
the Big Dipper. It was the first binary star system to be imaged
with a telescope. Spectroscopic observations show periodic
Doppler shifts in the spectra of Mizar A and B, indicating that they
are each binary stars. But they were too close to be directly
imaged - until 2 May 1996, when the NPOI produced the first
image of Mizar A. That image was the highest angular resolution
image ever made in optical astronomy. Since then, the NPOI has
observed Mizar A in 23 different positions over half the binary
orbit. These images have been combined here to make a movie
of the orbit. As a reference point, one component has been fixed
at the map center; in reality, the two stars are of comparable size
and revolve about a common central position.
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Stellar Masses
How massive are stars?
3
a
P 
M
2
• Most stars have masses calculated this way.
• Find:
– The more massive the star, the more luminous it is.
– The more massive the star, the hotter it is.
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Stellar Radii
How big are stars?
• We see stars have different
luminosities and different
temperatures.
• Stars have different sizes.
• If you know:
50 mas
– Distance
– Angular size
• Learn real size.
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Betelgeuse
• Angular size = 50 mas
• Parallax = 7.6 mas = 0.0076 arcsec
• Apparent mag = 0.6
• Distance = 1/parallax = 132 pc
• True size = distance * angular size = 1400 Rsol
• Absolute Mag = m – 5log(d/10pc) = -5
– Our sun M ~5, Betelgeuse = 10,000x luminosity
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Angular versus Linear
Supergiants, Giants and Dwarfs
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H-R Diagram
• Can order the stars by:
– Temperature (or spectral type)
– Luminosity (or absolute magnitude).
• And see where other qualities fall:
– Mass
– Radius
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Luminosity Class
• The roman numerals.
• Stars at same temp
can have different
luminosities.
• Corresponds to
different classes:
MS, giant,
supergiant.
I
V
III
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Concept Test
Which star is:
1. Hottest?
2. Coolest?
3. Faintest as seen
from Earth?
4. Most luminous?
Of Main Seq. Stars?
1. Most massive?
2. Most like the Sun?
Star
Spec
Type
m
M
A
F0 V
0.0
0.0
B
G2 V
10.0
4.4
C
K5 III
0.0
-2.0
D
F7 I
-1.0
-5.0
E
K3 V
5.0
6.5
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Homework #9
•
•
•
•
For Friday 10th:
Reread B16.1 – B16.5,
Read B16.6
Redo Problem 21, correct mistakes, give reasons.
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